Dependence of the stresses on grain orientations in hexagonal films

A thin polycrystalline film attached tightly to a thick substrate of different thermal expansion coefficients will experience thermal stresses when the temperature is changed during device fabrication and in service. Calculations of these stresses in various (h k l)-oriented grains relative to the film surface have been made for a polycrystalline film composed of the hexagonal metal Be, Cd, Co, Hf, Mg, Re, Ru, Sc, Ti, Y, Zr and Zn, respectively. For all these hexagonal films, the stresses σ1 and σ2 in plane of the film surface are equal only in (0 0 1)-oriented grains due to the highest six-fold rotation symmetry of the crystallographic Z-axis. Excepting σ1 of Be, Ru, Zr, Zn and σ2 of Cd, Zn, the maximum values of the film plane stresses σ1 and σ2 correspond to the (0 0 1)-oriented grains means that the significant reliability problems, such as, voiding, cracking, hillocking induced by the stresses may be taken place preferred in (0 0 1)-oriented grains.